تفسیر روح المعانی میں امام آلوسی کا منہج: ایک تحقیقی جائزہ

To understand the commentary of the Holy Qurân is a complex matter. Since the time of Holy Prophet Muhammad (S.A.W) till date the commentators have come to interpret the Holy Qurân for general public so that they should not face any difficulty to understand it. The Muhadithen made a separate chapter for Tafseer. In 19th century Imam Alusi (R.A) wrote a detailed commentary of the Holy Qurân. In this article I will produce a brief introduction of Imâm Alūsī (R.A) and his Tafseer. This paper touches the methodology of tafseer of Imam Alūsī (R.A) and the principles adopted by him.

Output Feedback Stabilization and Regulation for a Class of Under-Actuated Non-Minimum Phase Benchmark Nonlinear Systems

In this thesis, the problem of output feedback stabilization and regulation for a class of underactuated benchmark nonlinear systems is considered. The proposed method utilizes an extended high gain observer (EHGO)-based sliding mode control (SMC) technique to control a class of nonlinear systems which may have unstable zero dynamics. Starting with Lagrangian model of the system and using a suitable coordinate transformation, a generalized normal form representation is derived which decouples the system into its internal and external dynamics. The internal dynamics is utilized to derive an auxiliary system and the full-order EHGO thus obtained is used for estimation of derivative(s) of the system output that are further used in design of an output feedback control law. It is shown that the proposed output feedback controller stabilizes the system and convergence of estimated states is demonstrated with suitable selection of observer parameters. The proposed stabilizing control scheme is applied to two of the benchmark nonlinear systems, namely Inertia Wheel Pendulum (IWP), and Translational Oscillator with Rotational Actuator (TORA), in order to demonstrate the effectiveness of the technique by simulation. The technique is extended to further solve for the servomechanism (output regulation) problem for the class of under actuated non-minimum phase nonlinear systems under consideration. Towards this end, the control design is modified to include a ‘conditional servo compensator’ in order to track reference signals as well as reject disturbances while achieving stabilization and steady-state accuracy with a desired transient performance. The conditional servo compensator is utilized to regulate the controllable states by using SMC while neglectvi ing the internal states initially. The uncontrollable states of the system are estimated using an EHGO and the error signal is then used to synthesize a control input to stabilize the internal states by incorporating it in the sliding surface of the SMC design. The proposed control scheme is then applied to the Translational Oscillator with Rotational Actuator (TORA) system to validate the efficacy of the technique.